Hee-Sung Kim

Hee-Sung Kim

Toward a better understanding of deep learning.

A Simple and Efficient Measure of Loss Landscape Curvature

Published in ICML Workshop on High-dimensional Learning Dynamics (HiLD), 2026

Authors: Hee-Sung Kim, Sungyoon Lee

Venue: High-dimensional Learning Dynamics (HiLD), ICML 2026 Workshop

We revisit a scalable measure of loss-landscape curvature along the optimizer’s update direction. Its one-step descent boundary remains at twice the inverse learning rate across optimizers, including momentum and adaptive methods. We also propose finite-difference and KL-divergence estimators that reproduce Edge-of-Stability dynamics using only one or two additional forward passes per step, without Hessian-vector products.

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